Answer: First
Step-by-step explanation
Plug in x = 0 to solve for y.
3x + 4y = -12
3(0) + 4y = -12
4y = -12
y = -12/4
y = -3
The y intercept is located at (0,-3). This point is on the negative y axis which is the boundary between quadrants 3 and 4. If a non-vertical line passes through such a point, then this line must pass through quadrants 3 and 4.
Plug in y = 0 to solve for x.
3x + 4y = -12
3x + 4(0) = -12
3x = -12
x = -12/3
x = -4
The x intercept is (-4,0) which is on the boundary between quadrants 2 and 3.
Therefore, the line 3x+4y = -12 passes through quadrants 2, 3, and 4.
Quadrant 1 is the only quadrant that the line 3x+4y = -12 does not pass through. The graph below confirms this.